PCLAQSY

NAME

PCLAQSY - equilibrate a symmetric distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the scaling factors in the vectors SR and SC

SYNOPSIS

SUBROUTINE PCLAQSY(

UPLO, N, A, IA, JA, DESCA, SR, SC, SCOND,
AMAX, EQUED )

CHARACTER
EQUED, UPLO

INTEGER
IA, JA, N

REAL
AMAX, SCOND

INTEGER
DESCA( * )

REAL
SC( * ), SR( * )

COMPLEX
A( * )

PURPOSE

PCLAQSY equilibrates a symmetric distributed matrix
sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the scaling factors in the
vectors SR and SC.

Notes
=====

Each global data object is described by an associated description
vector. This vector stores the information required to establish
the mapping between an object element and its corresponding process
and memory location.

Let A be a generic term for any 2D block cyclicly distributed array.
Such a global array has an associated description vector DESCA.
In the following comments, the character _ should be read as
"of the global array".

NOTATION STORED IN EXPLANATION
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
M_A (global) DESCA( M_ ) The number of rows in the global
array A.
N_A (global) DESCA( N_ ) The number of columns in the global
array A.
MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
the rows of the array.
NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
row of the array A is distributed.
CSRC_A (global) DESCA( CSRC_ ) The process column over which the
first column of the array A is
distributed.
LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
array. LLD_A >= MAX(1,LOCr(M_A)).

Let K be the number of rows or columns of a distributed matrix,
and assume that its process grid has dimension p x q.
LOCr( K ) denotes the number of elements of K that a process
would receive if K were distributed over the p processes of its
process column.
Similarly, LOCc( K ) denotes the number of elements of K that a
process would receive if K were distributed over the q processes of
its process row.
The values of LOCr() and LOCc() may be determined via a call to the
ScaLAPACK tool function, NUMROC:

ARGUMENTS

Specifies whether the upper or lower triangular part of the
symmetric distributed matrix sub( A ) is to be referenced:
= 'U': Upper triangular
= 'L': Lower triangular

N (global input) INTEGER

The number of rows and columns to be operated on, i.e. the
order of the distributed submatrix sub( A ). N >= 0.

A (input/output) COMPLEX pointer into the local

memory to an array of local dimension (LLD_A,LOCc(JA+N-1)).
On entry, the local pieces of the distributed symmetric
matrix sub( A ). If UPLO = 'U', the leading N-by-N upper
triangular part of sub( A ) contains the upper triangular
part of the matrix, and the strictly lower triangular part
of sub( A ) is not referenced. If UPLO = 'L', the leading
N-by-N lower triangular part of sub( A ) contains the lower
triangular part of the matrix, and the strictly upper trian-
gular part of sub( A ) is not referenced.
On exit, if EQUED = 'Y', the equilibrated matrix:
diag(SR(IA:IA+N-1)) * sub( A ) * diag(SC(JA:JA+N-1)).

IA (global input) INTEGER

The row index in the global array A indicating the first
row of sub( A ).

JA (global input) INTEGER

The column index in the global array A indicating the
first column of sub( A ).

DESCA (global and local input) INTEGER array of dimension DLEN_.

The array descriptor for the distributed matrix A.

SR (local input) REAL array, dimension LOCr(M_A)

The scale factors for A(IA:IA+M-1,JA:JA+N-1). SR is aligned
with the distributed matrix A, and replicated across every
process column. SR is tied to the distributed matrix A.

SC (local input) REAL array, dimension LOCc(N_A)

The scale factors for sub( A ). SC is aligned with the dis-
tributed matrix A, and replicated down every process row.
SC is tied to the distributed matrix A.

SCOND (global input) REAL

Ratio of the smallest SR(i) (respectively SC(j)) to the
largest SR(i) (respectively SC(j)), with IA <= i <= IA+N-1
and JA <= j <= JA+N-1.